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skullpatrol
 2 years ago
Does 0.999...=1?
skullpatrol
 2 years ago
Does 0.999...=1?

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zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2.9999........ is not a number

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2have you taken calculus?

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2scroll down to number 4, its actaully an easy proof.

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2you will enjoy calculus:)

carson889
 2 years ago
Best ResponseYou've already chosen the best response.0Here is an algebraic proof of it: 10x = 9.999999... with x = 0.99999... 10x  x = 9.99999...  0.999999... 9x = 9 Thus, x = 1

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2This question was asked because I was trying to exaplin that inbetween any two numbers is another number, he then said what about .9999999.... and 1, i then tried to explain to him that .99999999.. was not a finite number, then we had this question posted:)

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2there is no amount of 9's that you can write after .9 that will make it equal to 1, but the limit as the amount of 9's goes to infinity is said to equal 1

ByteMe
 2 years ago
Best ResponseYou've already chosen the best response.0wait... doesn't 0.9999... = 9/10 + 9/100 + 9/1000 + .... an infinite bounded series?

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.2The number "0.9999..." can be "expanded" as: 0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2lol, read this. then you will see the point of the question http://openstudy.com/study#/updates/50ab1ceee4b06b5e49334d38

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.2So the formula proves that 0.9999... = 1.

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2but .99999...is not a number is the point of this topic

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.20.999999..... is a no. we have tp prove that it is equal to 1

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2its a number if you think about convergence, but you can never write 1 in the form .999999999999, read the last question and you will see the point im trying to make

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2its not a finite number.... it can be looked at as a sequence....at infinity then its a number. I told him that between any two numbers is another number, he then said what about .99999999999..... and 1, this is what followed.

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2Its an extended real number in the since that infinity is an extended real number....

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.2"But", some say, "there will always be a difference between 0.9999... and 1." Well, sort of. Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999...9 and 1. That is, if you do the subtraction, 1 – 0.999...9 will not equal zero. But the point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. (That's not a "criticism", per se; infinity is a messy topic.)

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2right and i dont think he has had calculus...

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2this started with density of rational/irational and archimedes principle on the real line

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2the point is, that there is an infinite amount of numbers between any two numbers a,b where a != b

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.2hahhaha.. we are just fighting you and me are absolutely right...it's a skull problem..right??

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.2right?? @zzr0ck3r

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.00.9999 is approximately equal to 1 but it is not exactly equal.. \[0.999 \approx 1 \qquad \qquad (0.999 \ne 1)\]

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.2got it @skullpatrol

mayankdevnani
 2 years ago
Best ResponseYou've already chosen the best response.2this question...lol

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.1can you provide a proof of this ... "This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)"

zzr0ck3r
 2 years ago
Best ResponseYou've already chosen the best response.2no, my analysis teacher said it two days ago. she said the elemnts between 0 and 1 have more mappings than 0infinity

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.1your teacher is either wrong or you have misquoted her

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.1the real numbers between 0 and 1 is the same size as the real numbers from 0 to infinity

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\[1  0.999\cdots = 0.000\cdots = 0\]
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